Math 521 (Finite Element Method)
- Course Details:
- Section 201, Spring 2016
- Lectures 9:30-11:00 in room Math 203.
- Instructor:
- Brian Wetton
- wetton@math.ubc.ca
- office: MATX 1107
- Office Hours:
- Tuesdays 2-3
- Fridays 11-12
- News:
- Assignment #5 posted, due April 15. Projects also due on that date.
- Assignment #4 posted, due Tuesday, March 22.
- Some additional course resources are listed below.
- Course Resources:
- Course outline
- Some texts:
- S.C. Brenner and R. Scott: The Mathematical Theory of Finite
Element Methods, second edition, Springer, 2002.
- D. Braess: Finite Elements: Theory, Fast Solvers, and Applications in Solid
Mechanics, third edition, Cambridge University Press, 2007.
- P.G. Ciarlet: The Finite Element Method for Elliptic
Problems, SIAM Classics, 2002; unabridged republication of the
book first published by North-Holland, 1978.
- A. Ern and J.-L. Guermond: Theory and Practice of Finite
Elements, Springer, 2004.
- H. Elman, D. Silvester and A. Wathen: Finite Elements
and Fast Iterative Solvers, Oxford University Press, 2005.
- V. Girault and P.-A. Raviart: Finite Element Methods
for Navier-Stokes Equations, Springer, 1986.
- C. Johnson: Numerical Solution of Partial Differential
Equations by the Finite Element Method, Dover, 2009; unabridged
republication of the lecture notes published in 1978.
- A. Quarteroni and A. Valli: Numerical Approximation of
Partial Differential Equations, Springer, 1996.
- Some online notes:
- Joseph Flaherty's
page. Look at the Course Notes link. I will be following his description
of error indicators for elliptic problems later in the course.
- Extensive notes
by Dominik Schoetzau. There are several sets of notes here bundled together.
- Course notes:
- Notes I
and sample MATLAB code for
problem #1. These notes
contain an introduction to finite difference methods.
- The video I showed in the first lecture is
here.
- An example for the procedure of
scaling
and non-dimensionalisation
that leads to the scaled problem #1 considered in the course.
- Some background notes on
Fourier Series and Transforms.
- Notes II (although
they are titled Notes III just to be confusing). These notes introduce
the notion of weak solution and the various function spaces needed
to describe the Finite Element Method.
- Notes III on the
basic ideas and convergence proof for conforming, Galerkin finite element
methods applied to a 1D boundary value problem.
- Notes IV on implementing
boundary conditions for the 1D boundary value problem.
- Notes V on
quadrature (approximate integration) methods.
- Notes VI
quadrature methods, part II.
- Notes VII
2D problems.
- Notes VIII
Analysis of 2D FEM.
- Notes IX
Domain approximation.
- Notes X
Approximating Neumann conditions. I am not sure now of the estimates on the
last two pages.
- Notes XI Time stepping
methods. The original hand written notes for this topic, with a final
discussion of some FEM details can be found
here.
- Notes XII
Multi-grid methods.
- Notes XIII
Additional notes on the significane of the residual in iterative linear
algebra methods for FE approximations.
- Notes XIV
Heirarchical Embedding Spaces.
- Notes XV
Efficient error estimates for elliptic problems.
- Notes XVI
Discontinuous Galerkin Methods.
- Notes XVII FEM for
incompressible flows.
- Some notes on topics that we probably won't cover this year:
handling nonlinear problems in
the FEM;
Conjugate Gradient Method.
Assignments:
- Assignment #1,
due Tuesday, January 26.
- Assignment #2,
due Tuesday, February 9.
- Assignment #3,
due Tuesday, March 1.
- Assignment #4,
due Tuesday, March 22. Note that in problem B3, The periodic solution is
the imaginary part of u exp(it) where u(x,y) is the complex solution of
the problem I wrote down.
- Assignment #5, due April
15.